Application of Maxima and Minima

As an example, the area of a rectangular lot, expressed in terms of its length and width, may also be expressed in terms of the cost of fencing. Thus the area can be expressed as A = f(x). The common task here is to find the value of x that will give a maximum value of A. To find this value, we set dA/dx = 0.

Steps in Solving Maxima and Minima Problems

  1. Identify the constant, say cost of fencing.
  2. Identify the variable to be maximized or minimized, say area A.
  3. Express this variable in terms of the other relevant variable(s), say A = f(x, y).
  4. If the function shall consist of more than one variable, expressed it in terms of one variable (if possible and practical) using the conditions in the problem, say A = f(x).
  5. Differentiate and equate to zero, dA/dx = 0.